A360534 Lexicographically earliest sequence of distinct prime numbers such that among each pair of consecutive terms, the decimal expansion of the smallest term appears in that of the largest term.

2, 23, 3, 13, 113, 11, 211, 2111, 22111, 322111, 3221, 32213, 2213, 22133, 622133, 6221, 62213, 362213, 5362213, 5, 53, 353, 3533, 33533, 333533, 33353, 233353, 233, 2333, 23333, 323333, 3233333, 32333333, 632333333, 6323, 86323, 863, 3863, 33863, 1338637, 7

Offset: 1

Author

Rémy Sigrist, Feb 10 2023

Keywords

• nonn
• base

Comments

This sequence is infinite:

- if a(n) < 10^k, then 10^(k+1) and 10*a(n) + 1 are coprime,

- so, by Dirichlet's theorem on arithmetic progressions, there are infinitely many prime numbers of the form k*10^(k+1) + 10*a(n) + 1, and we can extend the sequence.

If we consider positive integers instead of prime numbers, then we obtain the powers of 10 (A011557).

Examples

			The first terms are:
  n   a(n)    a(n) aligned
  --  ------  ------------
   1       2        2
   2      23        23
   3       3         3
   4      13        13
   5     113       113
   6      11       11
   7     211      211
   8    2111      2111
   9   22111     22111
  10  322111    322111
  11    3221    3221
  12   32213    32213
  13    2213     2213
  14   22133    22133
  15  622133   622133
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program

Crossrefs

Cf. A011557, A030456, A335043.

Programs

PARI

See Links section.